In this work, we presented the numerical investigation on the dynamics of fractional Langevin equation which is driven by a fractional Brownian motion and Caputo-Fabrizio fractional derivative operator were utilized. The order of fractional derivative was considered to be ν = 2 − 2H , where H ∈ (1/2, 1) is the Hurst’s index. In the context of numerical schemes, we present different numerical approaches such as the discrete sequence of finite difference, to simplify the second-order ordinary derivative, while for the fractional derivative term, we presented the discrete approximation using simple quadrature formula. Additionally, for overdamped case (without inertial term), we used the Adams-Bashforth method corresponding to the Caputo-Fabrizio fractional derivative. The convergence and stability analysis of the obtained numerical solution were established in this study.
Digital Object Identifier (DOI)
Azis Rangaig, Norodin and Magompara Conding, Rowaidah
"Numerics of Fractional Langevin Equation Driven by Fractional Brownian Motion Using Non-Singular Fractional Derivative,"
Progress in Fractional Differentiation & Applications: Vol. 6:
4, Article 2.
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol6/iss4/2